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Chapter 15: Problem 26

By what factor does \(\left[\mathrm{OH}^{-}\right]\) change when the \(\mathrm{pH}\) increases by 3\(?\) by 2\(?\) by 1 ? by 0.5\(?\)

Short Answer

Expert verified
The concentration of hydroxide ions, [OH-], increases by a factor of 1000 if the pH increases by 3, by a factor of 100 if the pH increases by 2, by a factor of 10 if the pH increases by 1, and by a factor of approximately 3.16 if the pH increases by 0.5.

Step by step solution

01

Understand that an increase in pH means an increase in [OH-]

When the pH increases, the pOH decreases (because pH + pOH =14 at 25°C). A decrease in pOH means an increase in [OH-] (because [OH-] = \(10^{-\text{pOH}}\)). Decreasing the power of 10 leads to an increase in the value.
02

Calculate the factor for a pH increase of 3

To calculate the factor, find the 10 to the power of the change in pH. So 10 to the power of 3 (the change in pH) is 1000. Thus, the [OH-] increases by a factor of 1000.
03

Repeat the calculation for other pH increases

Repeat Step 2 for the other given pH increases. For a pH increase of 2, 10 to the power of 2 is 100, so the [OH-] increases by a factor of 100. For a pH increase of 1, 10 to the power of 1 is 10, so the [OH-] increases by a factor of 10. For a pH increase of 0.5, 10 to the power of 0.5 (sqrt(10)) is approximately 3.16, so the [OH-] increases by a factor of approximately 3.16.

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